Is c the median of a, b and c ? (1) b - c = a (2) c = a how

Question

Is c the median of a, b and c ?

(1) b - c = a

(2) c = a

Bunuel · Answer

If a set has odd number of terms the median of the set is the middle number, when arranged in ascending or descending order; If a set has even number of terms the median of the set is the average of the two middle terms when arranged in ascending or descending order. So the median of the three numbers a, b and c would be the middle term, hence c would be the median in two cases: a\leq{c}\leq{b} or a\geq{c}\geq{b} .. (1) b - c = a --> clearly insufficient. If b=10, c=1, a=9=median, then answer would be NO but if b=10, c=9=median, and a=1, then answer would be YES. (2) c=a --> either the three numbers are c, c, b (in ascending order) --> media=c or the three numbers are b, c, c (in ascending order) --> median=c. Sufficient. Answer: B. Similar question: https://gmatclub.com/forum/ds6-93969.html?hilit=median Hope it helps.

scheol79 · Answer

B. Solved in 10 seconds because I solved a similar problem a few minutes ago. ds6-93969.html?hilit=median

jimmy86 · Answer

B 20 sec... was just studying number theory and then saw this question :-p thought at first that i was making a mistake but read the line "how quickly you solve this ? write down ur timings" and was sure that i was right :-D

aragonn · Answer

Official Solution: 
For the value of c to be the median, it needs to be the middle number of those 3 numbers.

Statement 1: There are many possible situations arising from this statement. In some, c is the median, but in others, it is not. Here are some examples:

Yes, c is the median:

a = 2, c = 3, b = 5
b - c = a
5 - 3 = 2

No, c is not the median:

c = 2, a = 3, b = 5
b - c = a
5 - 2 = 3

This statement is insufficient.

Statement 2: If two out of the three numbers in a set are equal, then those two numbers must represent the median. For example:

2, 2, 3
c, c, b
or
1, 2, 2
b, c, c

The only way b could go in the middle is if it also equals c. However, if all three numbers in a set are equal, then they all must be the median. So if a = b = c, the value of c is still the median. For example:

2, 2, 2
c, b, c

But since b = c, that's really the same as:

2, 2, 2
c, c, c

Thus, from this statement, we know that the value of c is always the median. This statement alone is sufficient.

AbenGeorge · Answer

Got confused on whether integer and +ve,-ve should be considered

bumpbot · Answer

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Is c the median of a, b and c ? (1) b - c = a (2) c = a how

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Is c the median of a, b and c ? (1) b - c = a (2) c = a how

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